Question

Find the greatest number that will divide $93,111$ and $129,$ leaving remainder 3 in each case.

Answer 1

Step: Find the greatest number
Since the remainder is $3$ in each case, decrease the remainder from $93,111$ and 9129) to find the required number.

So, $93-3=90$
$111-3=108$
$129-3=126$

$\therefore$ The greatest number will be $H.C.F.$ of $90,108$ and $126$
$H.C.F.$ of $90$ and $108$


$H.C.F.$ of $18$ and $126$

Here, the last division is $18.$
Thus, the $H.C.F.$ of $90,108$ and $126$ is $18$.
Hence, the greatest number that will divide $93,1112$ and $126$ is $18$.